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In mathematics, particularly in functional analysis, a bornological space is a type of space which, in some sense, possesses the minimum amount of structure needed to address questions of boundedness of sets and functions, in the same way that a topological space possesses the minimum amount of structure needed to address questions of continuity. Bornological spaces were first studied by Mackey. The name was coined by Bourbaki. ==Bornological sets== Let ''X'' be any set. A bornology on ''X'' is a collection ''B'' of subsets of ''X'' such that * ''B'' covers ''X'', i.e. * ''B'' is stable under inclusions, i.e. if ''A'' ∈ ''B'' and ''A′'' ⊆ ''A'', then ''A′'' ∈ ''B''; * ''B'' is stable under finite unions, i.e. if ''B''1, ..., ''B''''n'' ∈ ''B'', then Elements of the collection ''B'' are usually called bounded sets. However, if it is necessary to differentiate this formal usage of the term "bounded" with traditional uses, elements of the collection ''B'' may also be called ''bornivorous sets''. The pair (''X'', ''B'') is called a bornological set. A base of the bornology ''B'' is a subset of ''B'' such that each element of ''B'' is a subset of an element of . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「bornological space」の詳細全文を読む スポンサード リンク
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